% LLNCS DOCUMENT STYLE -- version 1.2
% for LaTeX version 2.09

% This style file is an adaptation of
% the original LaTeX article.sty

\typeout{Document Style `llncs', <version 1.2>}

\frenchspacing
\def~{\penalty\@M\kern3pt}

% Language dependant section
\def\literaturename{References}
\def\contentsname{Table of Contents}
\def\listoffiguresname{List of Figures}
\def\figurename{Fig.\thinspace}
\def\listoftablesname{List of Tables}
\def\tablename{Table }
\def\abstractname{Abstract.}
\newif\if@deutsch\@deutschfalse
%
\def\ds@deutsch{\typeout{German version}
\def\literaturename{Literatur}
\def\contentsname{Inhaltsverzeichnis}
\def\listoffiguresname{Abbildungsverzeichnis}
\def\figurename{Abb.\thinspace}
\def\listoftablesname{Tabellenverzeichnis}
\def\tablename{Tabelle }
\def\abstractname{Zusammenfassung.}
\@deutschtrue}

\def\thebibliography#1{\section*{\literaturename}\small\list
  {\arabic{enumi}.}{\settowidth\labelwidth{#1.}\leftmargin\labelwidth
    \advance\leftmargin\labelsep
    \usecounter{enumi}}
    \def\newblock{\hskip .11em plus .33em minus -.07em}
    \sloppy
    \sfcode`\.=1000\relax}

\def\ds@citeauthoryear{\def\thebibliography##1{\section*{\literaturename}%
    \small\list{}{\settowidth\labelwidth{}\leftmargin\parindent
    \itemindent=-\parindent
    \labelsep=\z@
    \usecounter{enumi}}%
    \def\newblock{\hskip .11em plus .33em minus -.07em}%
    \sloppy
    \sfcode`\.=1000\relax}%
    \def\@cite##1{##1}%
    \def\@lbibitem[##1]##2{\item[]\if@filesw
      {\def\protect####1{\string ####1\space}\immediate
    \write\@auxout{\string\bibcite{##2}{##1}}}\fi\ignorespaces}}%

\newif\if@envcountreset\@envcountresetfalse
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\def\ds@twoside{\@twosidetrue \@mparswitchtrue}
\def\ds@draft{\overfullrule
5pt}
\@options

\ds@twoside

\lineskip 1pt \normallineskip 1pt
\def\baselinestretch{1}

\def\@normalsize{\@setsize\normalsize{12pt}\xpt\@xpt
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\belowdisplayshortskip=2 mm plus4pt minus 4pt}

\mathchardef\Gamma="0100
\mathchardef\Delta="0101
\mathchardef\Theta="0102
\mathchardef\Lambda="0103
\mathchardef\Xi="0104
\mathchardef\Pi="0105
\mathchardef\Sigma="0106
\mathchardef\Upsilon="0107
\mathchardef\Phi="0108
\mathchardef\Psi="0109
\mathchardef\Omega="010A

\def\small{\@setsize\small{11pt}\ixpt\@ixpt
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\belowdisplayskip=2.5 mm plus5pt minus 3pt
\abovedisplayshortskip=0mm plus6pt minus 2pt
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\def\@listi{\leftmargin\leftmargini\topsep 4pt plus 2pt minus 2pt}}

\def\footnotesize{\@setsize\footnotesize{11pt}\ixpt\@ixpt
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\belowdisplayskip=2.5 mm plus5pt minus 3pt
\abovedisplayshortskip=0mm plus6pt minus 2pt
\belowdisplayshortskip=2 mm plus4pt minus 4pt
\def\@listi{\leftmargin\leftmargini\topsep 4pt plus 2pt minus 2pt}}

\def\scriptsize{\@setsize\scriptsize{8.4pt}\viipt\@viipt}

\def\tiny{\@setsize\tiny{6pt}\vpt\@vpt}
\def\large{\@setsize\large{13.2pt}\xipt\@xipt}
\def\Large{\@setsize\Large{14.4pt}\xiipt\@xiipt}
\def\LARGE{\@setsize\LARGE{16.8pt}\xivpt\@xivpt}
\def\huge{\@setsize\huge{22pt}\xxpt\@xxpt}
\def\Huge{\@setsize\Huge{30pt}\xxvpt\@xxvpt}
\@normalsize

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   \marginparwidth 107pt
\else \oddsidemargin 63pt \evensidemargin 63pt
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\textwidth 12.2truecm
\textheight 19.3truecm
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\def\vec#1{\mathchoice{\mbox{\boldmath$\displaystyle\bf#1$}}
{\mbox{\boldmath$\textstyle\bf#1$}}
{\mbox{\boldmath$\scriptstyle\bf#1$}}
{\mbox{\boldmath$\scriptscriptstyle\bf#1$}}}

\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
  \def\@svsec{}\else
  \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname\quad }\fi
  \@tempskipa #5\relax
   \ifdim \@tempskipa>\z@
  \begingroup #6\relax
  \noindent{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}
  \endgroup
    \csname #1mark\endcsname{#7}\addcontentsline
   {toc}{#1}{\ifnum #2>\c@secnumdepth \else
            \protect\numberline{\csname the#1\endcsname}\fi
          #7}\else
  \def\@svsechd{#6\hskip #3\@svsec #8\csname #1mark\endcsname
            {#7}\addcontentsline
             {toc}{#1}{\ifnum #2>\c@secnumdepth \else
               \protect\numberline{\csname the#1\endcsname}\fi
             #7}}\fi
  \@xsect{#5}}

\def\part{\par \addvspace{4ex} \@afterindentfalse \secdef\@part\@spart}

\def\@part[#1]#2{\ifnum \c@secnumdepth >\m@ne \refstepcounter{part}
\addcontentsline{toc}{part}{\thepart \hspace{1em}#1}\else
\addcontentsline{toc}{part}{#1}\fi { \parindent 0pt \raggedright
 \ifnum \c@secnumdepth >\m@ne \Large \bf
 Part\thepart\par\nobreak\fi\huge
\bf #2\markboth{}{}\par } \nobreak \vskip 3ex \@afterheading }

\def\@spart#1{{\parindent 0pt \raggedright
 \huge \bf
 #1\par} \nobreak \vskip 3ex \@afterheading }

\def\section{\@startsection {section}{1}{\z@}{-18pt plus -4pt minus
-4pt}{12pt plus 4pt minus 4pt}{\Large\bf\boldmath
\pretolerance=10000\relax\rightskip=0pt plus8em}}
\def\subsection{\@startsection{subsection}{2}{\z@}{-18pt plus-4pt minus
 -4pt}{8pt plus 4pt minus 4pt}{\normalsize\bf\boldmath
\pretolerance=10000\relax\rightskip=0pt plus8em}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-18pt plus-4pt
 minus -4pt}{-0.5em plus -.22em minus -0.1em}{\normalsize\bf\boldmath}}
\def\paragraph{\@startsection{paragraph}{4}{\z@}{-12pt plus -4pt minus
 -4pt}{-0.5em plus -.22em minus -0.1em}{\normalsize\it}}
\def\subparagraph#1{\typeout{LLNCS Warning: You should not use
\protect\subparagraph \space in this style.}\vskip0.5cm
You should not use $\backslash${\tt subparagraph} in this
style.\vskip0.5cm}

\setcounter{secnumdepth}{2}

\def\appendix{\par
 \setcounter{section}{0}
 \setcounter{subsection}{0}
 \def\thesection{\Alph{section}}}

\leftmargini 17pt     \leftmarginii 17pt
\leftmarginiii 17pt   \leftmarginiv 17pt
\leftmarginv 10pt       \leftmarginvi 10pt
\leftmargin\leftmargini \labelwidth\leftmargini
\advance\labelwidth-\labelsep
\labelsep 5pt
\parsep 0pt plus 1pt
\def\@listi{\leftmargin\leftmargini}
\def\@listii{\leftmargin\leftmarginii
 \labelwidth\leftmarginii\advance\labelwidth-\labelsep
 \topsep 0pt plus 1pt}
\def\@listiii{\leftmargin\leftmarginiii
 \labelwidth\leftmarginiii\advance\labelwidth-\labelsep
 \topsep 0pt plus 1pt}
\def\@listiv{\leftmargin\leftmarginiv
 \labelwidth\leftmarginiv\advance\labelwidth-\labelsep
 \topsep 0pt plus 1pt}
\def\@listv{\leftmargin\leftmarginv
 \labelwidth\leftmarginv\advance\labelwidth-\labelsep
 \topsep 0pt plus 1pt}
\def\@listvi{\leftmargin\leftmarginvi
 \labelwidth\leftmarginvi\advance\labelwidth-\labelsep
 \topsep 0pt plus 1pt}

\def\labelenumi{\arabic{enumi}.}
\def\theenumi{\arabic{enumi}}
\def\labelenumii{(\alph{enumii})}
\def\theenumii{\alph{enumii}}
\def\p@enumii{\theenumi}
\def\labelenumiii{\roman{enumiii}.}
\def\theenumiii{\roman{enumiii}}
\def\p@enumiii{\theenumi(\theenumii)}
\def\labelenumiv{\Alph{enumiv}.}
\def\theenumiv{\Alph{enumiv}}
\def\p@enumiv{\p@enumiii\theenumiii}

\def\labelitemi{\bf --}
\def\labelitemii{$\bullet$}
\def\labelitemiii{$\ast$}
\def\labelitemiv{$\cdot$}

\def\verse{\let\\=\@centercr
 \list{}{\itemsep\z@ \itemindent -1.5em\listparindent \itemindent
 \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}
\let\endverse\endlist
\def\quotation{\list{}{\listparindent 1.5em
 \itemindent\listparindent
 \rightmargin\leftmargin}\item[]}
\let\endquotation=\endlist
\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

\def\descriptionlabel#1{\hspace\labelsep \bf #1}
\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin
 \let\makelabel\descriptionlabel}}
\let\enddescription\endlist

\def\theequation{\arabic{equation}}

\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
 \else \newpage \fi \thispagestyle{empty}\c@page\z@}
\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}

\arraycolsep 1.4pt \tabcolsep 1.4pt \arrayrulewidth .4pt \doublerulesep
2pt
\tabbingsep \labelsep

\skip\@mpfootins = \skip\footins
\fboxsep = 3pt \fboxrule = .4pt

\newcounter{part}
\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]

\def\thepart{\Roman{part}}
\def\thesection {\arabic{section}}
\def\thesubsection {\thesection.\arabic{subsection}}
\def\thesubsubsection {\thesubsection.\arabic{subsubsection}}
\def\theparagraph {\thesubsubsection.\arabic{paragraph}}

\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{3}

\def\tableofcontents{\section*{\contentsname}
 \@starttoc{toc}}
\def\l@part#1#2{\addpenalty{\@secpenalty}
 \addvspace{2.25em plus 1pt} \begingroup
 \@tempdima 3em \parindent \z@ \rightskip \@pnumwidth \parfillskip
-\@pnumwidth
 {\Large \bf \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}}\par
 \nobreak \endgroup}
%
\def\numberline#1{\advance\hangindent by\@tempdima%
\hbox to\@tempdima{\hss#1\enspace}}
%
\def\bf@dottedtocline#1#2#3#4#5{\ifnum #1>\c@tocdepth \else
  \vskip \z@ plus .2pt
  {\leftskip #2\relax \rightskip \@tocrmarg \parfillskip -\rightskip
    \parindent #2\relax\@afterindenttrue
   \interlinepenalty\@M
   \leavevmode
   \@tempdima #3\relax \advance\leftskip \@tempdima \hbox{}\hskip
   -\leftskip
{\bf#4}\nobreak\leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern \@dotsep
       mu$}\hfill \nobreak \hbox to\@pnumwidth{\hfil\rm #5}\par}\fi}
%
\def\l@section{\vskip2mm\bf@dottedtocline{1}{0em}{1.7em}}
\def\l@subsection{\@dottedtocline{2}{1.7em}{2.3em}}
\def\l@subsubsection{\@dottedtocline{3}{4em}{2em}}
\def\l@paragraph{\@dottedtocline{4}{6em}{2em}}
\def\l@subparagraph{\@dottedtocline{5}{8em}{2em}}
\def\listoffigures{\section*{\listoffiguresname\markboth
 {\listoffiguresname}{\listoffiguresname}}\@starttoc{lof}}
\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
\def\listoftables{\section*{\listoftablesname\markboth
 {\listoftablesname}{\listoftablesname}}\@starttoc{lot}}
\let\l@table\l@figure

\def\endthebibliography{\endlist\normalsize}

\newif\if@restonecol
\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi
\columnseprule \z@
\columnsep 35pt\twocolumn[\section*{Index}]
 \markboth{Index}{Index}\thispagestyle{plain}\parindent\z@
 \parskip\z@ plus .3pt\relax\let\item\@idxitem}
\def\@idxitem{\par\hangindent 40pt}
\def\subitem{\par\hangindent 40pt \hspace*{20pt}}
\def\subsubitem{\par\hangindent 40pt \hspace*{30pt}}
\def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi}
\def\indexspace{\par \vskip 10pt plus 5pt minus 3pt\relax}

\def\footnoterule{\kern-3\p@\hrule width 2 true cm\kern 2.6\p@}

\long\def\@makefntext#1{\@setpar{\@@par\@tempdima \hsize
  \advance\@tempdima-1em\parshape \@ne 1em\@tempdima}\par
  \parindent 1em\noindent \hbox to \z@{\hss$^{\@thefnmark}$\ }#1}

\setcounter{topnumber}{2}
\def\topfraction{.9}
\setcounter{bottomnumber}{1}
\def\bottomfraction{.3}
\setcounter{totalnumber}{3}
\def\textfraction{.15}
\def\floatpagefraction{.85}
\setcounter{dbltopnumber}{2}
\def\dbltopfraction{.85}
\def\dblfloatpagefraction{.85}

\long\def\@makecaption#1#2{
 \vskip 10pt
 \setbox\@tempboxa\hbox{{\bf #1} #2}
 \ifdim \wd\@tempboxa >\hsize \unhbox\@tempboxa\par \else \hbox
to\hsize{\hfil\box\@tempboxa\hfil}
 \fi\vskip5pt}

\long\def\@caption#1[#2]#3{\addcontentsline{\csname
  ext@#1\endcsname}{#1}{\protect\numberline{\csname
  the#1\endcsname}{\ignorespaces #2}}\par
  \begingroup
    \@parboxrestore
    \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
  \endgroup}

\newcounter{figure}
\def\thefigure{\@arabic\c@figure}

\def\fps@figure{htbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{\figurename\thefigure.}
\def\figure{\small\rm\@float{figure}}
\def\endfigure{\vskip-5pt\end@float}
\@namedef{figure*}{\@dblfloat{figure}}
\@namedef{endfigure*}{\end@dblfloat}

\newcounter{table}
\def\thetable{\@arabic\c@table}
\def\fps@table{htbp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{\tablename\thetable.}
\def\table{\small\rm\@float{table}}
\let\endtable\end@float
\@namedef{table*}{\@dblfloat{table}}
\@namedef{endtable*}{\end@dblfloat}

% LaTeX does not provide a command to enter the authors institute
% addresses. The \institute command is defined here.

\newcounter{@inst}
\newcounter{@auth}

\def\institute#1{\gdef\@institute{#1}}

\def\institutename{\par
 \begingroup
 \parskip=\z@
 \parindent=\z@
 \setcounter{@inst}{1}%
 \def\and{\par\stepcounter{@inst}%
 \noindent$^{\the@inst}$\enspace\ignorespaces}%
 \setbox0=\vbox{\def\thanks##1{}\@institute}%
 \ifnum\c@@inst=1\relax
 \else
   \setcounter{footnote}{\c@@inst}%
   \setcounter{@inst}{1}%
   \noindent$^{\the@inst}$\enspace
 \fi
 \ignorespaces
 \@institute\par
 \endgroup}

\def\@thanks{}

\def\@fnsymbol#1{\ifcase#1\or\star\or{\star\star}\or{\star\star\star}%
   \or \dagger\or \ddagger\or
   \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger
   \or \ddagger\ddagger\else\@ctrerr\fi\relax}

\def\inst#1{\unskip$^{#1}$}

\def\subtitle#1{\gdef\@subtitle{#1}}
\def\@subtitle{}

\def\maketitle{\par
 \begingroup
 \parindent=\z@
 \def\thefootnote{\fnsymbol{footnote}}
 \if@twocolumn
 \twocolumn[\@maketitle]
 \else \newpage
 \global\@topnum\z@ \@maketitle \fi\thispagestyle{empty}\@thanks
 \endgroup
 \let\maketitle\relax
 \let\@maketitle\relax
 \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\gdef\@subtitle{}%
 \let\thanks\relax}

\def\@maketitle{\newpage
 \begin{center}%
 {\LARGE \bf\boldmath
  \pretolerance=10000
  \@title \par}\vskip .8cm
\if!\@subtitle!\else {\Large \bf\boldmath
  \vskip -.65cm
  \pretolerance=10000
  \@subtitle \par}\vskip .8cm\fi
{\normalsize\rm\lineskip .5em
\@author\vskip.35cm}
 {\small\rm\institutename}
 \end{center}%
 }

\mark{{}{}}

% Define `abstract' environment
\def\abstract{%
\list{}{\advance\topsep by0.35cm\relax\small\rm
 \leftmargin=1cm
 \labelwidth=\z@
 \listparindent=\z@
 \itemindent\listparindent
 \rightmargin\leftmargin}\item[\hskip\labelsep\bf\abstractname]}
\let\endabstract=\endlist
\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

\def\ps@headings{\def\@evenhead{}%
\let\@oddhead\@evenhead
\let\@evenfoot\@evenhead
\let\@oddfoot\@evenhead
\def\sectionmark##1{}%
\def\subsectionmark##1{}}
\def\ps@myheadings{\let\@mkboth\@gobbletwo
\def\@oddhead{\hbox{}\small\rm\rightmark \hfil\thepage}%
\def\@oddfoot{}\def\@evenhead{\small\rm\thepage\hfil
\leftmark\hbox {}}%
\def\@evenfoot{}\def\sectionmark##1{}\def\subsectionmark##1{}}

\def\today{\ifcase\month\or
 January\or February\or March\or April\or May\or June\or
 July\or August\or September\or October\or November\or December\fi
 \space\number\day, \number\year}

\ps@headings \pagenumbering{arabic} \onecolumn
\if@twoside\else\raggedbottom\fi

% new environments and theorems
% borrowed form the LTMP-style of Springer-Verlag
% designed by Dr. Christoph Ender
%
% define the new theorem like environments
% define a new style of environments where it is possible to define
% the font % used as the theorem name and the fontfamily for the text.
%
% \newstytheorem{name}{thefont}{txtfont}{Text}[Counter]
% \newstytheorem{name}{thefont}{txtfont}[oldname]{Text}
%
% #1 - name of theorem
% #2 - theorem font
% #3 - text font
%
\def\newstytheorem#1#2#3{%
\@ifnextchar[{\che@othm{#1}{#2}{#3}}{\che@nthm{#1}{#2}{#3}}}
%
% #1 - name of theorem
% #2 - theorem font
% #3 - text font
% #4 - text string of thorem name
%
\def\che@nthm#1#2#3#4{%
\@ifnextchar[{\che@xnthm{#1}{#2}{#3}{#4}}{\che@ynthm{#1}{#2}{#3}{#4}}}
%
% #1 - name of theorem
% #2 - theorem font
% #3 - text font
% #4 - text string of thorem name
% #5 - add theorem counter to reset list of another counter
%
\def\che@xnthm#1#2#3#4[#5]{\expandafter
\@ifdefinable\csname #1\endcsname
{\@definecounter{#1}\if@envcountreset\@addtoreset{#1}{#5}\fi
\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
\global\@namedef{#1}{\che@thm{#1}{#4}{#2}{#3}}\global
\@namedef{end#1}{\@endtheorem}}}
%
% #1 - name of theorem
% #2 - theorem font
% #3 - text font
% #4 - text string of thorem name
%
\def\che@ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
{\@definecounter{#1}%
\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
\global\@namedef{#1}{\che@thm{#1}{#2}{#3}{#4}}\global
\@namedef{end#1}{\@endtheorem}}}
%
% change oldthm if oldname in specification is '*'
% then don't use a counter
% #1 - countername
% #2 - theorem font
% #3 - text font
% #4 - counter used
% #5 - string containing theorem name to print
%
\def\che@othm#1#2#3[#4]#5{\expandafter\@ifdefinable
\csname#1\endcsname%
{\@@othm@{#1}{#2}{#3}{#4}{#5}\global\@namedef{end#1}{\@endtheorem}}}
%
\def\@@othm@#1#2#3#4#5{\if *#4{\global\@namedef{the#1}{\relax}
\global\@namedef{#1}{\@bthm@{}{#5}{#2}{#3}}}\else
{\global\@namedef{the#1}{\@nameuse{the#4}}% define the counter
\global\@namedef{#1}{\che@thm{#4}{#5}{#2}{#3}}}\fi}
%
% new defs for theorem environment che 17-MAR-1989
% it improves the option possible
%
% #1 - countername  = theorem name
% #2 - string containing theorem name to print
% #3 - theorem font
% #4 - text font
\def\che@thm#1#2#3#4{\@ifnextchar({\@athm{#1}{#2}{#3}{#4}}{%
\@ifnextchar *{\@bthm{#1}{#2}{#3}{#4}}%
{\@@thm{#1}{#2}{#3}{#4}}}}
%
% \begin{thm}(A.1)[test]      results in:
% \end{thm}                               thm A.1 (test) ....
% #1 - theorem
% #2 - string of theorem name
% #3 - font for theorem name and label
% #4 - Text font
% #5 - is the new label
% #6 - optional string
%
\def\@athm#1#2#3#4(#5){\@ifnextchar[{%
\@aythm{#1}{#2}{#3}{#4}{#5}}{\@axthm{#1}{#2}{#3}{#4}{#5}}}
\def\@axthm#1#2#3#4#5{\@@locthmlab{#1}{#5}%
\@begintheorem{#2}{#5}{#3}{#4}\ignorespaces}
\def\@aythm#1#2#3#4#5[#6]{\@@locthmlab{#1}{#5}%
\fuh@opargbegintheorem{#2}{#5}{#6}{#3}{#4}\ignorespaces}
%
% \begin{thm}*[xytest]        results in:
% \end{thm}                               thm (xytest) ....
% #1 - theorem
% #2 - string of theorem name
% #3 - font for theorem name and label
% #4 - Text font
% #5 - optional string
%
\def\@bthm@#1#2#3#4{\@ifnextchar[{\@bythm{#1}{#2}{#3}{#4}}{%
\@bxthm{#1}{#2}{#3}{#4}}}
\def\@bthm#1#2#3#4*{\@ifnextchar[{\@bythm{#1}{#2}{#3}{#4}}{%
\@bxthm{#1}{#2}{#3}{#4}}}
\def\@bxthm#1#2#3#4{\if !#1!\relax\else\@@locthmlab{#1}{}\fi
\@@begintheorem{#2}{#3}{#4}\ignorespaces}
\def\@bythm#1#2#3#4[#5]{%
\@@opargbegintheorem{#2}{#3}{#4}{#5}\ignorespaces}
%
% define local label
%   if no number or a user specified label occured
%
\def\@@locthmlab#1#2{\expandafter\def\csname the#1\endcsname{#2}
\let\@chetempa\protect\def\protect{\noexpand\protect\noexpand}%
\edef\@currentlabel{\csname p@#1\endcsname\csname the#1\endcsname}%
\let\protect\@chetempa}
%
% #1 - counter = theorem name
% #2 - string with name
% #3 - font for theorem name and label
% #4 - font for text
\def\@@thm#1#2#3#4{\refstepcounter
    {#1}\@ifnextchar[{\che@ythm{#1}{#2}{#3}{#4}}{%
    \che@xthm{#1}{#2}{#3}{#4}}}
%
\def\che@xthm#1#2#3#4{\che@begintheorem{#2}{\csname
the#1\endcsname}{#3}{#4}\ignorespaces}
\def\che@ythm#1#2#3#4[#5]{\che@opargbegintheorem{#2}{\csname
       the#1\endcsname}{#5}{#3}{#4}\ignorespaces}
%
% #1 - name of theorem
% #2 - label string
% #3 - font for name and lable
% #4 - text fomt
%
\def\che@begintheorem#1#2#3#4{#4\trivlist\item[\hskip\labelsep
#3#1\ts #2.]}
%
% #1 - name of theorem
% #2 - label string
% #3 - additonal text
% #4 - font for name and lable
% #5 - text fomt
%
\def\che@opargbegintheorem#1#2#3#4#5{#5\trivlist
\item[\hskip\labelsep#4#1\ts #2\ #3.]}
%
\def\fuh@opargbegintheorem#1#2#3{\it \trivlist
      \item[\hskip \labelsep{\bf #1\ #2\ (#3).}]}
%
\def\@@begintheorem#1#2#3{#3\trivlist\item[\hskip\labelsep
#2#1.]}
\def\@@opargbegintheorem#1#2#3#4{#3\trivlist\item[\hskip\labelsep
#2#1 #4.]}

\if@deutsch
\newstytheorem{theorem}{\bf}{\it}{Theorem}[section]
\newstytheorem{example}{\it}{\rm}{Beispiel}[section]
\newstytheorem{proposition}{\bf}{\it}[theorem]{Proposition}
\newstytheorem{corollary}{\bf}{\it}[theorem]{Korollar}
\newstytheorem{lemma}{\bf}{\it}[theorem]{Lemma}
\newstytheorem{proof}{\it}{\rm}[*]{Beweis}
\newstytheorem{definition}{\bf}{\rm}[theorem]{Definition}
\newstytheorem{remark}{\it}{\rm}[*]{Anmerkung}
\newstytheorem{exercise}{\it}{\rm}[theorem]{\"{U}bung}
\newstytheorem{problem}{\it}{\rm}[theorem]{Problem}
\newstytheorem{solution}{\it}{\rm}[theorem]{L\"{o}sung}
\newstytheorem{note}{\it}{\rm}[theorem]{Hinweis}
\newstytheorem{question}{\it}{\rm}[theorem]{Frage}
\else
\newstytheorem{theorem}{\bf}{\it}{Theorem}[section]
\newstytheorem{example}{\it}{\rm}{Example}[section]
\newstytheorem{proposition}{\bf}{\it}[theorem]{Proposition}
\newstytheorem{corollary}{\bf}{\it}[theorem]{Corollary}
\newstytheorem{lemma}{\bf}{\it}[theorem]{Lemma}
\newstytheorem{proof}{\it}{\rm}[*]{Proof}
\newstytheorem{definition}{\bf}{\rm}[theorem]{Definition}
\newstytheorem{remark}{\it}{\rm}[*]{Remark}
\newstytheorem{exercise}{\it}{\rm}[theorem]{Exercise}
\newstytheorem{problem}{\it}{\rm}[theorem]{Problem}
\newstytheorem{solution}{\it}{\rm}[theorem]{Solution}
\newstytheorem{note}{\it}{\rm}[theorem]{Note}
\newstytheorem{question}{\it}{\rm}[theorem]{Question}
\fi

\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}}
\def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil
\penalty50\hskip1em\null\nobreak\hfil\squareforqed
\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}

\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip
\halign{\hfil
$\displaystyle##$\hfil\cr\gets\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets
\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets
\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
\gets\cr\to\cr}}}}}
\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr
\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr
\noalign{\vskip0.9pt}=\cr}}}}}
\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr
\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr
\noalign{\vskip0.9pt}=\cr}}}}}
\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip
\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\noalign{\vskip-1pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\noalign{\vskip-0.8pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\noalign{\vskip-0.3pt}<\cr}}}}}
\def\bbbr{{\rm I\!R}} %reelle Zahlen
\def\bbbm{{\rm I\!M}}
\def\bbbn{{\rm I\!N}} %natuerliche Zahlen
\def\bbbf{{\rm I\!F}}
\def\bbbh{{\rm I\!H}}
\def\bbbk{{\rm I\!K}}
\def\bbbp{{\rm I\!P}}
\def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l}
{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}}
\def\bbbc{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}}
\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}}
\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
T$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox
to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox
to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox
to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}}
\def\bbbs{{\mathchoice
{\setbox0=\hbox{$\displaystyle     \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox
to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle        \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox
to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle      \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
to0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
to0pt{\kern0.55\wd0\vrule height0.45\ht0\hss}\box0}}}}
\def\bbbz{{\mathchoice {\hbox{$\sf\textstyle Z\kern-0.4em Z$}}
{\hbox{$\sf\textstyle Z\kern-0.4em Z$}}
{\hbox{$\sf\scriptstyle Z\kern-0.3em Z$}}
{\hbox{$\sf\scriptscriptstyle Z\kern-0.2em Z$}}}}
\def\ts{\thinspace}

\if@deutsch
\def\typeset{\vfill\small\noindent Dieser Artikel wurde mit
dem \LaTeX\ Makro-Paket und dem LLNCS-Style formatiert.\par}
\else
\def\typeset{\vfill\small\noindent This article was processed using
the \LaTeX\ macro package with LLNCS style\par}
\fi

\def\enddocument{\par\typeset
\@checkend{document}\clearpage\begingroup
\if@filesw \immediate\closeout\@mainaux
\def\global\@namedef##1##2{}\def\newlabel{\@testdef r}%
\def\bibcite{\@testdef b}\@tempswafalse\makeatletter\input \jobname.aux
\if@tempswa \@warning{Label(s) may have changed. Rerun to get
cross-references right}\fi\fi\endgroup\deadcycles\z@\@@end}
\endinput
